She goes and takes their order -> "su pedido" o "sus pedidos"

Hola Shafagh

This is because the sentence is saying "Marta goes and takes their order." - order, in singular, therefore you need the noun in the singular form "su pedido".

To use the plural it would have to say "Marta goes and takes their orders.", but this would imply that they had more than one order, which is not the case. 

I hope this clarifies it.

Saludos

Inma